Theorems · Theorem · commutative algebra
IsLocalRing.ResidueField.map_map
∀ {R : Type u_1} {S : Type u_2} {T : Type u_3} [inst : CommRing R] [inst_1 : IsLocalRing R] [inst_2 : CommRing S]
[inst_3 : IsLocalRing S] [inst_4 : CommRing T] [inst_5 : IsLocalRing T] (f : R →+* S) (g : S →+* T)
(x : IsLocalRing.ResidueField R) [inst_6 : IsLocalHom f] [inst_7 : IsLocalHom g],
(IsLocalRing.ResidueField.map g) ((IsLocalRing.ResidueField.map f) x) = (IsLocalRing.ResidueField.map (g.comp f)) x- Cited by
- 0 results in Mathlib
- Foundations
- Depth 97 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- RingHomstatement and proof · cited by 10,189
- RingHom.compstatement · cited by 899
- IsLocalRingstatement and proof · cited by 339
- DFunLike.congr_funproof · cited by 288
- IsLocalRing.ResidueFieldstatement and proof · cited by 156
- IsLocalHomstatement and proof · cited by 100
- IsLocalRing.ResidueField.mapstatement · cited by 16
- IsLocalRing.ResidueField.map_compproof · cited by 3
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